Bayesian Principal Component Regression model with spatial effects for forest inventory under small field sample size

Abstract: Remote sensing observations are extensively used for analysis of environmental variables. These variables often exhibit spatial correlation, which has to be accounted for in the calibration models used in predictions, either by direct modelling of the dependencies or by allowing for spatially correlated stochastic effects. Another feature in many remote sensing instruments is that the derived predictor variables are highly correlated, which can lead to unnecessary model over-training and at worst, singularities in the estimates. Both of these affect the prediction accuracy, especially when the training set for model calibration is small. To overcome these modelling challenges, we present a general model calibration procedure for remotely sensed data and apply it to airborne laser scanning data for forest inventory. We use a linear regression model that accounts for multicollinearity in the predictors by principal components and Bayesian regularization. It has a spatial random effect component for the spatial correlations that are not explained by a simple linear model. An efficient Markov chain Monte Carlo sampling scheme is used to account for the uncertainty in all the model parameters. We tested the proposed model against several alternatives and it outperformed the other linear calibration models, especially when there were spatial effects, multicollinearity and the training set size was small.